Twitter is full of this, as you would expect. I don't follow many, but those that I do are all full of horror and posting 'anti-gun ownership' tweets. Looking at their feeds though, there are an awful lot of "prize my gun from my cold dead hands" type stuff and an awful lot from (I assume) NRA members talking about this tragedy being nothing more than 'post birth abortion'.

When you have sentiment like that being posted, I don't see how banning gun ownership will ever happen 
I thought this was interesting though - from a post that was retweeted by Marti Noxon, it talks about Japan's policy for gun ownership - and the hoops the people have to jump through to get them:
To get a gun in Japan, first, you have to attend an all-day class and pass a written test, which are held only once per month. You also must take and pass a shooting range class. Then, head over to a hospital for a mental test and drug test (Japan is unusual in that potential gun owners must affirmatively prove their mental fitness), which you'll file with the police. Finally, pass a rigorous background check for any criminal record or association with criminal or extremist groups, and you will be the proud new owner of your shotgun or air rifle. Just don't forget to provide police with documentation on the specific location of the gun in your home, as well as the ammo, both of which must be locked and stored separately. And remember to have the police inspect the gun once per year and to re-take the class and exam every three years.
Rather than ban guns (which is never going to happen) maybe the US needs to look at more stringent methods of controlling ownership.